SEO Question on domain changes

I have a page I created for an organization a few years ago and if you search Church Residency on Google it's in the top 3 listings. They've moved to have their residency info on a separate domain now and now I'm wondering what the best practice would be moving forward for their old URL.
Should I redirect the old URL to the new domain since the old URL ranks higher OR delete the older page so the new site will rise in search rankings? Currently the new domain is about 20 listings down right now. It's only been live for a few weeks though. Feels like the redirect option would hurt SEO in the long run?